Re: reverse engineering of acoustic sources

[Georg Essl <gessl@xxxxxxxxxxxxxxxx>]

Hi Pierre,

I do agree that inverse problems are hard.  Though I would argue that the
inverse spectral problem of the linear wave equation is much easier than
the same for the articulatory tract, which is clearly not a as simple a
situation.

- Georg

On Sat, 31 Jan 2004, Pierre Divenyi wrote:

> Date: Sat, 31 Jan 2004 10:43:50 -0800
> From: Pierre Divenyi <pdivenyi@ebire.org>
> To: Georg Essl <gessl@CS.Princeton.EDU>, AUDITORY@LISTS.MCGILL.CA
> Subject: Re: reverse engineering of acoustic sources
>
> Pardon my bringing in a negative view, but I have serious doubts that a
> unique solution to any specific wave can be found. Although I have never
> delved into the mathematics of it, I only know of the problem in phonetics,
> where the acoustic-to-articulatory inversion has been extensively
> investigated, only to come up with the answer that solutions require very
> restrictive initial and boundary values and functions. I can't imagine that
> the acoustic-to-musical instrument problem should be any easier to solve.
> But correct me if I am wrong.
>
> Pierre Divenyi
>
> At 01:13 PM 1/31/2004 -0500, Georg Essl wrote:
> >Hi Jim,
> >
> >  I think it's probably fair to say that the pure mathematicians who work
> >on this don't necessarily have typical real-world acoustical situations in
> >mind. The formalisms tend to isolate one problem and tend to try to make a
> >dent there. So 2-D structures (membranes) and 3-D (rooms) cases are
> >usually treated separately.
> >
> >As for excitations, these are usually not featured prominently, though
> >they are definitely there implicitly at least. I'd say in the papers that
> >I've read very often harmonic drivers (force-sustained) are assumed, but
> >not necessarily. It helps to bring the wave equation into reduced
> >Helmholtz form, which is convenient. It's a spatial problem only rather
> >than a temporal and spatial problem that way. In other formalisms, the
> >dynamic response in general usually with respect to the geometry of the
> >situation is considered in which case asymptotic arguments pop up (often
> >by lack of a better method). Asymptotic in this setting means that an
> >approximate form is assumed whose error shrinks with some parameter
> >becoming large, e.g. typically for high frequencies. Of course if the
> >situations could be treated directly, one would.
> >
> >But despite all the simplications and reductions, the story isn't simple
> >(and not fully understood), which is I guess the point I wanted to make
> >with respect to the paragraph of the SciAm article.
> >
> >- Georg
> >
> >On Sat, 31 Jan 2004, beauchamp james w wrote:
> >
> > > Date: Sat, 31 Jan 2004 09:38:22 -0600 (CST)
> > > From: beauchamp james w <jwbeauch@ux1.cso.uiuc.edu>
> > > To: gessl@CS.Princeton.EDU
> > > Cc: auditory@lists.mcgill.ca
> > > Subject: Re: reverse engineering of acoustic sources
> > >
> > > Dear Georg,
> > >
> > > Thank you for your wonderful response to my question.
> > >
> > > I wonder if any of the mathematical solutions to this problem take
> > > into account directivity and room responses and whether they work
> > > for forced sustained vibrations (e.g., clarinet) as opposed to
> > > free vibrations (e.g., a drum).
> > >
> > > Jim Beauchamp
> > >
>
>
>